GSoC 2025: Alternative Spin representation

[RichRick1]

📚 Package Description and Impact

This project aims to enhance the Model Hamiltonian package by implementing a new spin representation system. The current implementation's limitations in handling certain spin operators will be addressed through a more flexible and comprehensive approach, enabling support for general XYZ Heisenberg models.

👷 What will you do?

You will implement a direct spin modeling system using creation and annihilation operators. The key components include:

• Implementation of spin operators ($S_k^+$, $S_k^-$, $S^Z_k$)
• Handling of maximum seniority states
• Support for different $N_\alpha$ and $N_{\beta}$ electron configurations
• Verification of spin algebra commutation relations

🏁 Expected Outcomes

1. Implement new spin operator representations

$$ \begin{align*} S_k^+ &= a_{k\alpha}^\dagger a_{k\beta} \\ S_k^- &= a_{k\beta}^\dagger a_{k\alpha} \\ S^Z_k &= \tfrac{1}{2}\left(a_{k\alpha}^\dagger a_{k\alpha}-a_{k\beta}^\dagger a_{k\beta} \right) \end{align*} $$

2. Develop support for general XYZ Heisenberg models
3. Write comprehensive documentation for the new spin representation system

Required skills	Python, Linear Algebra, Quantum Mechanics
Preferred skills	Experience with quantum chemistry, familiarity with spin operators
Project size	90 hours, Small
Difficulty	Medium 🤓

🙋 Mentors

Valerii Chuiko	valerachuiko_at_gmail_dot_com	@RichRick1
Paul Ayers	ayers_at_mcmaster_dot_ca	@PaulWAyers

[asterisk-ragavan]

Hi, @RichRick1 I'm a Python developer, I would like to contribute to this project.

[RichRick1]

Hi @asterisk-ragavan! Please send me an email and I will provide some additional resources on how you can contribute to the project.

[typhonshambo]

hi @RichRick1! I have sent you an email regarding this PR, including my proposed approach for the implementation. Please let me know if you need any further details. Looking forward to your response!

This project matching what im doing currently, including my one of my coursework based on Quantum Sensing and Metrology, so i decided to make a short outlined approach what to do!